Question

Write the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients. 1/(x³-1) (x²-1)

Answer 1

The partial fraction decomposition of the function 1/(x³-1)(x²-1) can be written as A/(x-1) + B/(x²+x+1) + C/(x-1) + D/(x+1).

Step-by-step explanation:

The given function can be written as:

1/(x³-1) (x²-1)

To find the partial fraction decomposition of the function, we need to factor the denominator.

Factoring the denominator gives us:

1/[(x-1)(x²+x+1)(x-1)(x+1)]

Next, we express the function as the sum of its partial fractions:

1/[(x-1)(x²+x+1)(x-1)(x+1)] = A/(x-1) + B/(x²+x+1) + C/(x-1) + D/(x+1)

Where A, B, C, and D are coefficients that we will determine later.

This is the form of the partial fraction decomposition of the function.